Number field search results

Note: Search results may be incomplete due to uncomputed quantities: local_algs (140954 objects)

Degree	Signature	Class number	Class group structure	CM field
Ramified prime count	Ramified	Unramified primes	Galois group	Is Galois
Discriminant	Root discriminant	Regulator	Intermediate field	$p$-adic completions
Monogenic	Index	Ines. \(p\)

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Label	Polynomial	Degree	Signature	Discriminant	Ram. prime count	Root discriminant	CM field	Galois	Monogenic	Galois group	Class group	Unit group torsion	Unit group rank	Regulator
2.2.73.1	x^2 - x - 18	$2$	[2,0]	$73$	$1$	$8.54400374532$		✓	✓	$C_2$ (as 2T1)	trivial	$2$	$1$	$7.66669041926$
2.0.219.1	x^2 - x + 55	$2$	[0,1]	$-\,3\cdot 73$	$2$	$14.7986485869$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.292.1	x^2 + 73	$2$	[0,1]	$-\,2^{2}\cdot 73$	$2$	$17.0880074906$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.584.1	x^2 + 146	$2$	[0,1]	$-\,2^{3}\cdot 73$	$2$	$24.1660919472$	✓	✓	✓	$C_2$ (as 2T1)	$[16]$	$2$	$0$	$1$
2.2.584.1	x^2 - 146	$2$	[2,0]	$2^{3}\cdot 73$	$2$	$24.1660919472$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$5.66986903216$
2.2.876.1	x^2 - 219	$2$	[2,0]	$2^{2}\cdot 3\cdot 73$	$3$	$29.5972971739$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$4.99716661688$
2.0.1387.1	x^2 - x + 347	$2$	[0,1]	$-\,19\cdot 73$	$2$	$37.2424488991$	✓	✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$0$	$1$
2.0.1679.1	x^2 - x + 420	$2$	[0,1]	$-\,23\cdot 73$	$2$	$40.9756024971$	✓	✓	✓	$C_2$ (as 2T1)	$[52]$	$2$	$0$	$1$
2.0.1752.1	x^2 + 438	$2$	[0,1]	$-\,2^{3}\cdot 3\cdot 73$	$3$	$41.8568990729$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 4]$	$2$	$0$	$1$
2.2.1752.1	x^2 - 438	$2$	[2,0]	$2^{3}\cdot 3\cdot 73$	$3$	$41.8568990729$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$6.37331687747$
2.0.2555.1	x^2 - x + 639	$2$	[0,1]	$-\,5\cdot 7\cdot 73$	$3$	$50.5470078244$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 6]$	$2$	$0$	$1$
2.2.2701.1	x^2 - x - 675	$2$	[2,0]	$37\cdot 73$	$2$	$51.9711458407$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$14.5970417147$
2.2.2993.1	x^2 - x - 748	$2$	[2,0]	$41\cdot 73$	$2$	$54.7083174664$		✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$1$	$7.87321690985$
2.0.4015.1	x^2 - x + 1004	$2$	[0,1]	$-\,5\cdot 11\cdot 73$	$3$	$63.3640276498$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 10]$	$2$	$0$	$1$
2.2.4161.1	x^2 - x - 1040	$2$	[2,0]	$3\cdot 19\cdot 73$	$3$	$64.5058136915$		✓	✓	$C_2$ (as 2T1)	$[8]$	$2$	$1$	$10.0073970139$
2.2.4453.1	x^2 - x - 1113	$2$	[2,0]	$61\cdot 73$	$2$	$66.7308024828$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$18.3092773289$
2.2.4745.1	x^2 - x - 1186	$2$	[2,0]	$5\cdot 13\cdot 73$	$3$	$68.8839603972$		✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$1$	$12.7595668778$
2.0.4891.1	x^2 - x + 1223	$2$	[0,1]	$-\,67\cdot 73$	$2$	$69.9356847396$	✓	✓	✓	$C_2$ (as 2T1)	$[20]$	$2$	$0$	$1$
2.2.5037.1	x^2 - x - 1259	$2$	[2,0]	$3\cdot 23\cdot 73$	$3$	$70.9718253957$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$4.26248144465$
2.0.5183.1	x^2 - x + 1296	$2$	[0,1]	$-\,71\cdot 73$	$2$	$71.9930552206$	✓	✓	✓	$C_2$ (as 2T1)	$[80]$	$2$	$0$	$1$
2.2.5548.1	x^2 - 1387	$2$	[2,0]	$2^{2}\cdot 19\cdot 73$	$3$	$74.4848977981$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$14.9210600617$
2.2.5621.1	x^2 - x - 1405	$2$	[2,0]	$7\cdot 11\cdot 73$	$3$	$74.9733285909$		✓	✓	$C_2$ (as 2T1)	$[6]$	$2$	$1$	$4.31731028833$
2.0.5767.1	x^2 - x + 1442	$2$	[0,1]	$-\,73\cdot 79$	$2$	$75.9407663907$	✓	✓	✓	$C_2$ (as 2T1)	$[36]$	$2$	$0$	$1$
2.2.6205.1	x^2 - x - 1551	$2$	[2,0]	$5\cdot 17\cdot 73$	$3$	$78.7718223732$		✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$1$	$11.5412796586$
2.2.6497.1	x^2 - x - 1624	$2$	[2,0]	$73\cdot 89$	$2$	$80.6039701255$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$13.617335191$
2.0.6643.1	x^2 - x + 1661	$2$	[0,1]	$-\,7\cdot 13\cdot 73$	$3$	$81.5046010971$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 6]$	$2$	$0$	$1$
2.2.6716.1	x^2 - 1679	$2$	[2,0]	$2^{2}\cdot 23\cdot 73$	$3$	$81.9512049942$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$8.11969616438$
2.2.7081.1	x^2 - x - 1770	$2$	[2,0]	$73\cdot 97$	$2$	$84.1486779456$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$78.6044327304$
2.2.7665.1	x^2 - x - 1916	$2$	[2,0]	$3\cdot 5\cdot 7\cdot 73$	$4$	$87.5499857224$		✓	✓	$C_2$ (as 2T1)	$[2, 6]$	$2$	$1$	$8.16108943131$
2.2.7957.1	x^2 - x - 1989	$2$	[2,0]	$73\cdot 109$	$2$	$89.2020179144$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$9.08602352465$
2.0.8103.1	x^2 - x + 2026	$2$	[0,1]	$-\,3\cdot 37\cdot 73$	$3$	$90.0166651237$	✓	✓	✓	$C_2$ (as 2T1)	$[4, 12]$	$2$	$0$	$1$
2.0.8687.1	x^2 - x + 2172	$2$	[0,1]	$-\,7\cdot 17\cdot 73$	$3$	$93.204077164$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 42]$	$2$	$0$	$1$
2.0.8979.1	x^2 - x + 2245	$2$	[0,1]	$-\,3\cdot 41\cdot 73$	$3$	$94.7575854483$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 12]$	$2$	$0$	$1$
2.0.9271.1	x^2 - x + 2318	$2$	[0,1]	$-\,73\cdot 127$	$2$	$96.2860322165$	✓	✓	✓	$C_2$ (as 2T1)	$[60]$	$2$	$0$	$1$
2.2.10001.1	x^2 - x - 2500	$2$	[2,0]	$73\cdot 137$	$2$	$100.004999875$		✓	✓	$C_2$ (as 2T1)	$[16]$	$2$	$1$	$5.29834236561$
2.2.10220.1	x^2 - 2555	$2$	[2,0]	$2^{2}\cdot 5\cdot 7\cdot 73$	$4$	$101.094015649$		✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$1$	$9.37822487382$
2.0.10439.1	x^2 - x + 2610	$2$	[0,1]	$-\,11\cdot 13\cdot 73$	$3$	$102.171424577$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 62]$	$2$	$0$	$1$
2.2.10585.1	x^2 - x - 2646	$2$	[2,0]	$5\cdot 29\cdot 73$	$3$	$102.883429181$		✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$1$	$44.6027621132$
2.0.10804.1	x^2 + 2701	$2$	[0,1]	$-\,2^{2}\cdot 37\cdot 73$	$3$	$103.942291681$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 24]$	$2$	$0$	$1$
2.2.10877.1	x^2 - x - 2719	$2$	[2,0]	$73\cdot 149$	$2$	$104.292856898$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$10.2819924779$
2.0.11096.1	x^2 + 2774	$2$	[0,1]	$-\,2^{3}\cdot 19\cdot 73$	$3$	$105.337552658$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 28]$	$2$	$0$	$1$
2.2.11096.1	x^2 - 2774	$2$	[2,0]	$2^{3}\cdot 19\cdot 73$	$3$	$105.337552658$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$10.8183773031$
2.0.11315.1	x^2 - x + 2829	$2$	[0,1]	$-\,5\cdot 31\cdot 73$	$3$	$106.371988794$	✓	✓	✓	$C_2$ (as 2T1)	$[2, 22]$	$2$	$0$	$1$
2.0.11972.1	x^2 + 2993	$2$	[0,1]	$-\,2^{2}\cdot 41\cdot 73$	$3$	$109.416634933$	✓	✓	✓	$C_2$ (as 2T1)	$[4, 12]$	$2$	$0$	$1$
2.2.12045.1	x^2 - x - 3011	$2$	[2,0]	$3\cdot 5\cdot 11\cdot 73$	$4$	$109.749715262$		✓	✓	$C_2$ (as 2T1)	$[2, 2]$	$2$	$1$	$6.77764529642$
2.2.12629.1	x^2 - x - 3157	$2$	[2,0]	$73\cdot 173$	$2$	$112.378823628$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$10.7739646863$
2.2.13213.1	x^2 - x - 3303	$2$	[2,0]	$73\cdot 181$	$2$	$114.947814246$		✓	✓	$C_2$ (as 2T1)	$[2]$	$2$	$1$	$23.6726563695$
2.0.13359.1	x^2 - x + 3340	$2$	[0,1]	$-\,3\cdot 61\cdot 73$	$3$	$115.58114033$	✓	✓	✓	$C_2$ (as 2T1)	$[4, 24]$	$2$	$0$	$1$
2.0.13432.1	x^2 + 3358	$2$	[0,1]	$-\,2^{3}\cdot 23\cdot 73$	$3$	$115.896505556$	✓	✓	✓	$C_2$ (as 2T1)	$[4, 8]$	$2$	$0$	$1$
2.2.13432.1	x^2 - 3358	$2$	[2,0]	$2^{3}\cdot 23\cdot 73$	$3$	$115.896505556$		✓	✓	$C_2$ (as 2T1)	$[4]$	$2$	$1$	$20.9802774121$

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